Raymond had driven two girls, an 11-year-old student and her 9-year-old sister to Canobie Lake Park in Salem, N.H., twice in August 2007.

Raymond touched the 11-year-old girl’s buttocks three times during the first trip and once again during the second trip, the appeals court wrote in its 16-page decision.

“The district court determined that the buttocks-touching incidents were intentional and carried out for the purpose of sexual gratification,” Judge Bruce Selya of the U.S. Court of Appeals for the First Circuit in Boston wrote in the court’s Wednesday decision.

Judge Hornby pointed to four pieces of evidence in particular to support his guilty finding:

— The victim’s testimony.

— The testimony of other students who observed Raymond with the victim on a group bus trip.

— The testimony of another victim who said Raymond touched her buttocks at school in October 2007.

— A videotaped interview of Raymond by an Auburn police detective during which Raymond talked about his “physical urge to touch young girls’ buttocks.”

Raymond appealed to the federal law court, claiming the lower trial court erred on three points.

Through his attorney, Richard Hartley, Raymond said the trial judge “improperly admitted evidence of both his contact with the victim during the June 2007 bus trip and his inappropriate conduct with another girl in October of that year.”

Raymond also challenged the lower court’s decision to restrict cross-examination of Auburn Police Department Detective Chad Syphers and to not allow Hartley a reasonable opportunity to impeach him.

The last point of appeal was Raymond’s claim that Hornby shouldn’t have sentenced him to more than the 10-year statutory minimum. By doing so, Raymond claims his constitutional right to be free from cruel and unusual punishment was violated.

Prosecutors had sought a 17½-year sentence. The maximum possible sentence was life.

According to court records, the victim kept quiet about Raymond touching her when it happened. In October 2007, when Raymond’s arrest on the state charge involving another girl became public, Raymond called the 11-year-old girl’s mother. The mother then called the school to complain about that phone call, and the school contacted police. Police interviewed the girl that day, and later arranged for her to be evaluated at a sexual assault crisis center in Lewiston. It was there that the girl revealed the circumstances of the touching during the New Hampshire trips.

She testified that it took her so long to tell someone because she was scared and embarrassed by the incidents, and remained scared and embarrassed.

In making his ruling, Hornby found that Raymond “had motivation to lie” to police and to the court because “his liberty and music teaching career both are at stake.”

Raymond’s attempts, Hornby found, “to explain away the damaging statements that he made about his interest in young girls to the Auburn detective during the videotaped interview were wholly unpersuasive,” and that his court testimony of the circumstances of contact between himself and the girl were not credible.

In 2008, Raymond was tried and convicted in Androscoggin County Superior Court in Auburn on five charges: two counts of unlawful sexual touching and three counts of assault. The three girls involved were music students of Raymond at the time of the incidents in April 2005 and September and October 2007.

One girl was a first-grader at East Auburn Community School, another was a second-grader at Park Avenue Elementary School and the third was a fifth-grader at Webster Intermediate School.

The judge allowed the prior Superior Court conviction to be presented during the federal trial, over Raymond’s objection, to show motive and intent, according to the ruling.

During the period that those crimes took place, Raymond was a teacher at Park Avenue and East Auburn elementary schools. He also was an assistant marching band instructor at Leavitt Area High School in Turner, founder of the Central Maine Children’s Theater Project and an instructor for the Central Maine Children’s Chorus.